The Optimal Correlation Detector?

Correlation detectors are now used routinely in seismology to detect occurrences of signals bearing close resemblance to a reference waveform. They facilitate the detection of low-amplitude signals in significant background noise that may elude detection using energy detectors, and they associate a detected signal with a source location. Many seismologists use the fully normalized correlation coefficient $C$ between the template and incoming data to determine a detection. This is in contrast to other fields with a longer tradition for matched filter detection where the theoretically optimal statistic $C^2$ is typical. We perform a systematic comparison between the detection statistics $C$ and $C|C|$, the latter having the same dynamic range as $C^2$ but differentiating between correlation and anti-correlation. Using a database of short waveform segments, each containing the signal on a 3-component seismometer from one of 51 closely spaced explosions, we attempt to detect P- and S- phase arrivals for all events using short waveform templates from each explosion as a reference event. We present empirical statistics of both $C$ and $C|C|$ traces and demonstrate that $C|C|$ detects confidently a higher proportion of the signals than $C$ without evidently increasing the likelihood of triggering erroneously. We recall from elementary statistics that $C^2$, also called the coefficient of determination, represents the fraction of the variance of one variable which can be explained by another variable. This means that the fraction of a segment of our incoming data that could be explained by our signal template decreases almost linearly with $C|C|$ but diminishes more rapidly as $C$ decreases. In most situations, replacing $C$ with $C|C|$ in operational correlation detectors may improve the detection sensitivity without hurting the performance-gain obtained through network stacking. It may also allow a better comparison between single-template correlation detectors and higher order multiple-template subspace detectors which, by definition, already apply an optimal detection statistic.

Beyond Correlation: A Path‐Invariant Measure for Seismogram Similarity

Similarity search is a popular technique for seismic signal processing, with template matching, matched filters, and subspace detectors being utilized for a wide variety of tasks, including both signal detection and source discrimination. Traditionally, these techniques rely on the cross‐correlation function as the basis for measuring similarity. Unfortunately, seismogram correlation is dominated by path effects, essentially requiring a distinct waveform template along each path of interest. To address this limitation, we propose a novel measure of seismogram similarity that is explicitly invariant to path. Using Earthscope’s USArray experiment, a path‐rich dataset of 207,291 regional seismograms across 8452 unique events is constructed, and then employed via the batch‐hard triplet loss function, to train a deep convolutional neural network that maps raw seismograms to a low‐dimensional embedding space, where nearness on the space corresponds to nearness of source function, regardless of path or recording instrumentation. This path‐agnostic embedding space forms a new representation for seismograms, characterized by robust, source‐specific features, which we show to be useful for performing both pairwise event association as well as template‐based source discrimination with a single template.